Geodesic
The Spectral Side of Stable Local Trace Formula
Documenta mathematica, Tome 24 (2019), pp. 303-329.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Let $G$ be a connected quasi-split reductive group over $\mathbb{R}$, and more generally, a quasi-split $K$-group over $\mathbb{R}$. Arthur had obtained the formal formula for the spectral side of the stable local trace formula, by using formal substitute of Langlands parameters. In this paper, we construct the spectral side of the stable local trace formula and endoscopic local trace formula directly for quasi-split $K$-groups over $\mathbb{R}$, by incorporating the works of Shelstad. In particular we give the explicit expression for the spectral side of the stable local trace formula, in terms of Langlands parameters.
Classification : 22E45, 22E46
Keywords: stabilization, endoscopy, local trace formula, transfer factors 
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     title = {The {Spectral} {Side} of {Stable} {Local} {Trace} {Formula}},
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Mok, Chung Pang; Peng, Zhifeng. The Spectral Side of Stable Local Trace Formula. Documenta mathematica, Tome 24 (2019), pp. 303-329. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a53/